.svg){kind=logo}
EXACT BIAS OF ESTIMATOR FOR UAR(1) MODEL WITH MISSING OBSERVATIONS
Keywords:
unconditional ordinary least square estimator, unconditional modification weighted symmetricDOI:
https://doi.org/10.17654/0972361723005Abstract
In this paper, a new form of the estimator of unconditional autoregressive model of order one UAR(1) with missing observations has been derived by using unconditional ordinary least squares (UOLS) and unconditional modification weighted symmetric (UMWS) estimators in two cases for unconditional autoregressive model with missing observations when the initial value 
Also, a modification of the formula of weighted symmetric of UAR(p) model with missing observations has been suggested as an extension of Park and Fuller [15], which provides an exact formula for the bias of the parameter estimator of the first order autoregressive process for (UOLS) and (UMWS) estimators. A comparison between (UOLS), (UMWSI) and (UMUSII) estimators using unconditional AR(1) model with missing observation is conducted through a Monte-Carlo simulation at various sample sizes and different proportions of missing observations considering the absolute bias as a criterion of comparison.
Received: October 14, 2022; Revised: December 22, 2022; Accepted: December 27, 2022; Published: December 31, 2022
References
M. M. Abdelwahab, On parameter estimation of time series models with missing observations, Ph.D. Thesis, Institute of Statistical Studies and Research, Cairo University, 2016.
M. M. Abdelwahab and M. K. A. Issa, Forms of the moments of AR(P) model with missing observations, The Egyptian Statistical Journal 63 (2019), 39-44.
H. F. Azmy, Statistical inference of the parameters in autoregressive models, Ph.D. Thesis, Institute of Statistical Studies and Research, Cairo University, 2019.
G. E. Box and G. M. Jenkins, Time Series Analysis, Control, and Forecasting, San Francisco, CA: Holden Day, 1976.
A. L. Breton and D. T. Pham, On the bias of the least squares estimator for the first order autoregressive process, Ann. Inst. Statist. Math. 41 (1989), 555-563.
J. Ding, L. Han and X. Chen, Time series AR modeling with missing observations based on the polynomial transformation, Mathematical and Computer Modelling 51 (2010), 527-536.
W. Dunsmuir and P. M. Robinson, Estimation of time series models in the presence of missing data, Journal of the American Statistical Association 76 (1981), 560-568.
S. M. El-Sayed, A. A. El-Sheikh, M. K. A. Issa and H. F. M. A. Azmy, A closed form of biased AR(1) model, Advances and Applications in Statistics 50 (2017), 191-199.
M. A. Enany, M. K. Issa and A. A. Gad, A suggested estimator of AR(1) model with missing observations, Thailand Statistic 19 (2021).
G. M. Farias, New unit root test for autoregressive time series, Ph.D. Thesis, North Carolina University, 1992.
D. P. Hasza, A note on maximum likelihood estimation for the first-order autoregressive process, Comm. Statist. Theory Methods 9 (1980), 1411-1415.
M. K. A. Issa, New estimator for AR(1) model with missing observations, Journal of University of Shanghai for Science and Technology 23 (2021), 147-159.
M. K. A. Issa, Weighted least squares estimation for AR(1) model with incomplete data, Mathematics and Statistics 10 (2022), 342-357.
M. K. A. Issa and M. M. Abdelwahab, Estimation of AR(1) panel data model with missing observations, Journal of Advances and Applications in Statistics 63 (2020), 109-117.
H. Park and W. Fuller, Alternative estimators and unit root tests for the autoregressive process, Journal of Time Series Analysis 16 (1995), 415-429.
E. Parzen, On spectral analysis with missing observations and amplitude modulation, Sankhya: The Indian Journal of Statistics 25 (1963), 383-392.
L. R. Shenton and H. D. Vinod, Closed forms for asymptotic bias and variance in autoregressive models with unit roots, J. Comput. Appl. Math. 61 (1995), 231-243.
K. Takeuchi, A comment on recent development of economic data analysis, at the 63rd Annual Meeting of Japan Statistical Society, 1996.
W. W. Wei, Time Series Analysis Univariate and Multivariate Methods, 2nd ed., Addison-Wesley, New York, 2006.
A. H. Youssef, A performance of alternative predictors for the unit root process, Interstat. Journal (2006).
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
